Question

Factorise the Quadratic polynomial: \[{{a}^{2}}-\left( b+5 \right)a+5b\].

Answer 1

Hint: In this problem, we have to factorize the given expression. We can first multiply the term a inside the bracket, we will get an expression. We can then take the common terms from the first two terms and the last two terms, where we can take the common term ‘a’ from the first two terms and -5 from the last two terms. We can again take the common term a-b and write the remaining terms to get the factored form

Complete step-by-step solution:
Here we have to find the factors for the given expression,
 \[{{a}^{2}}-\left( b+5 \right)a+5b\]
We can now multiply the term ‘a’ inside the brackets, we get
\[= {{a}^{2}}-ab-5a+5b\]
We can then take the common terms from the first two terms and the last two terms, where we can take the common term ‘a’ from the first two terms and -5 form the last two terms, we get
\[= a\left( a-b \right)-5\left( a-b \right)\]
We can see that the above step has a common factor, we can now take and write it as,
\[= \left( a-5 \right)\left( a+b \right)\]
Therefore, the factors of the given expression \[{{a}^{2}}-\left( b+5 \right)a+5b\] is \[\left( a-5 \right)\left( a+b \right)\].

Note: We should always remember that, if we multiply the resulting two factors, then we should get the given expression. We should also remember that, we can factorize an expression with variables by taking common terms outsides one by one and then write the final answer. We should form the given expression in a proper format to take common terms from it.